Results 11 to 20 of about 892,665 (298)
The Electronic Journal of Combinatorics, 2019 We say that a graph $H$ is planar unavoidable if there is a planar graph $G$ such that any red/blue coloring of the edges of $G$ contains a monochromatic copy of $H$, otherwise we say that $H$ is planar avoidable. That is, $H$ is planar unavoidable if there is a Ramsey graph for $H$ that is planar. It follows from the Four-Color Theorem and a result of
Axenovich, M. +3 more
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Planarity of Streamed Graphs [PDF]
Theoretical Computer Science, 2015 In this paper we introduce a notion of planarity for graphs that are presented in a streaming fashion. A $\textit{streamed graph}$ is a stream of edges $e_1,e_2,...,e_m$ on a vertex set $V$. A streamed graph is $ω$-$\textit{stream planar}$ with respect to a positive integer window size $ω$ if there exists a sequence of planar topological drawings $Γ_i$
Giordano Da Lozzo, Ignaz Rutter
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Planar median graphs and cubesquare-graphs [PDF]
Discrete Applied Mathematics, 2023 Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. In this paper we provide several novel characterizations of planar median graphs.
Carsten R. Seemann +3 more
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On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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On the planar edge-length ratio of planar graphs
Journal of Computational Geometry, 2020 The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight ...
Manuel Borrazzo, Fabrizio Frati
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A Planarity Criterion for Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2015 It is proven that a connected graph is planar if and only if all its cocycles with at least four edges are "grounded" in the graph. The notion of grounding of this planarity criterion, which is purely combinatorial, stems from the intuitive idea that with planarity there should be a linear ordering of the edges of a cocycle such that in the two ...
Kosta Dosen, Zoran Petric
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Untangling a Planar Graph [PDF]
Discrete & Computational Geometry, 2008 A straight-line drawing $δ$ of a planar graph $G$ need not be plane, but can be made so by \emph{untangling} it, that is, by moving some of the vertices of $G$. Let shift$(G,δ)$ denote the minimum number of vertices that need to be moved to untangle $δ$. We show that shift$(G,δ)$ is NP-hard to compute and to approximate.
Xavier Goaoc +5 more
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Upward Planar Drawings with Three and More Slopes
Journal of Graph Algorithms and Applications, 2023 The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing.
Jonathan Klawitter, Johannes Zink
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An SPQR-tree-like embedding representation for level planarity
Journal of Computational Geometry, 2023 An SPQR-tree is a data structure that efficiently represents all planar embeddings of a connected planar graph. It is a key tool in a number of constrained planarity testing algorithms, which seek a planar embedding of a graph subject to some given set
Guido Brückner, Ignaz Rutter
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Exploiting planarity in separation routines for the symmetric traveling salesman problem [PDF]
, 2008 At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut.
Adam N. Letchford +5 more
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